Two-scale topology design optimization of stiffened or porous plate subject to out-of-plane buckling constraint
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admin
Date
2019-03-05 20:42
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3751
Title
Authors
Gengdong Cheng, Liang Xu
Journal
Structural and Multidisciplinary Optimization, (2016) 54:1283–1296
Keywords
Two-scale analysis; Concurrent topology optimization; Buckling constraints; NIAH method
Abstract
This paper studies maximum out-of-plane buckling load design of thin bending plates for a given amount of material. Two kinds of plates are considered. One is made of periodic homogeneous porous material. Another is uniformly stiffened solid plate. The plate material, thickness, design domain of its middle plane and boundary conditions are given. The pattern of prescribed in-plane external load or displacements along the part of boundaries, which move freely, is given. Both plate topology and micro-structural topology of porous material or stiffener layout are concurrently optimized. The artificial element material densities in both macro and micro-scale are chosen as design variables. The volume preserving nonlinear density filter is applied to obtain the blackwhite optimum topology and comparison of its different sensitivities is made to show the reason for oscillation during optimization process in Appendix. The new numerical implementation of asymptotic homogenization method (NIAH, Cheng (Acta Mech Sinica 29(4): 550–556, 2013) and Cai (Int J Solids Struct 51(1), 284–292, 2014) is applied to homogenization of periodic plate structures and analytic sensitivity analysis of effective stiffness with respect to the topological design variables in both macro-scale and micro-scale. On basis of that, this paper implements the sensitivity analysis of out-of-plane buckling load by using commercial FEA software and enables the application of gradient-based search algorithm in optimization. Several numerical implementation details are discussed. Three numerical examples are given to
show the validity of this method.
Link
https://link.springer.com/article/10.1007/s00158-016-1542-y
Two-scale topology design optimization of stiffened or porous plate subject to out-of-plane buckling constraint
Authors
Gengdong Cheng, Liang Xu
Journal
Structural and Multidisciplinary Optimization, (2016) 54:1283–1296
Keywords
Two-scale analysis; Concurrent topology optimization; Buckling constraints; NIAH method
Abstract
This paper studies maximum out-of-plane buckling load design of thin bending plates for a given amount of material. Two kinds of plates are considered. One is made of periodic homogeneous porous material. Another is uniformly stiffened solid plate. The plate material, thickness, design domain of its middle plane and boundary conditions are given. The pattern of prescribed in-plane external load or displacements along the part of boundaries, which move freely, is given. Both plate topology and micro-structural topology of porous material or stiffener layout are concurrently optimized. The artificial element material densities in both macro and micro-scale are chosen as design variables. The volume preserving nonlinear density filter is applied to obtain the blackwhite optimum topology and comparison of its different sensitivities is made to show the reason for oscillation during optimization process in Appendix. The new numerical implementation of asymptotic homogenization method (NIAH, Cheng (Acta Mech Sinica 29(4): 550–556, 2013) and Cai (Int J Solids Struct 51(1), 284–292, 2014) is applied to homogenization of periodic plate structures and analytic sensitivity analysis of effective stiffness with respect to the topological design variables in both macro-scale and micro-scale. On basis of that, this paper implements the sensitivity analysis of out-of-plane buckling load by using commercial FEA software and enables the application of gradient-based search algorithm in optimization. Several numerical implementation details are discussed. Three numerical examples are given to
show the validity of this method.
Link
https://link.springer.com/article/10.1007/s00158-016-1542-y